A dialysis device contains a series of fluid channels separated by a permeable membrane. Convective clearance of solutes from blood in the device is determined by the transmembrane pressure in the device. Typically, the fluid in adjacent channels flows in opposite directions and the channels have a non-linear fluid volume profile along their lengths. Increasing the convective clearance requires decreasing the fluid volume in the channel carrying blood, which can result in an unsafe hematocrit level in the channel. Therefore, it is desirable to increase the amount of convective clearance within a compact dialysis device while maintaining safe hematocrit levels throughout the blood channel.